We study covering codes of permutations with the l∞-metric. We provide a general code construction, which uses smaller building-block codes. We study cyclic transitive groups as building blocks, determining their exact covering radius, and showing linear-time algorithms for finding a covering codeword. We also bound the covering radius of relabeled cyclic transitive groups under conjugation. In...

SolC. P. and T. Zaslavsky, The covering radius of the cycle code of a graph, Discrete Applied Mathematics 45 (I 993) 63-70. The cycle code of a graph is the binary linear span of the characteristic vectors of circuits. We exploit a connection between the covering radius of this code and minimum T-joins. We obtain a lower bound on the covering radius which is met with equality when the graph is ...

Let X be a compact Riemann surface of genus ≥ 2 of constant negative curvature −1. An extremal disk is an embedded (resp. covering) disk of maximal (resp. minimal) radius. A surface containing an extremal disk is an extremal surface. This paper gives formulas enumerating extremal surfaces of genus ≥ 4 up to isometry. We show also that the isometry group of an extremal surface is always cyclic o...

We apply polynomial techniques (i.e., which invole polynomials) to obtain lower and upper bounds on the covering radius of spherical designs as function their dimension, strength, cardinality. In terms inner products we improve due Fazekas Levenshtein propose new bounds. Our approach involves certain signed measures whose corresponding series orthogonal polynomials are positive definite up a (a...

This paper gives lower and upper bounds on the covering radius of codes over $\mathbb{Z}_{p^2}$ with respect to Lee distance. We also determine the covering radius of various Repetition codes over $\mathbb{Z}_{p^2}.$